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Underidentification, Structural Estimation, and Forecasting

Ta-Chung Liu

Abstract

Since the publication of Haavelmo's well-known papers on simultaneous equation estimation in 1943-44, the literature on this subject has dealt mainly with overidentified relationships. Practically all the econometric models estimated by the simultaneous equation approach are overidentified, the contention being that economic theory or a priori information would require the exclusion of a sufficient number of variables from a given relationship so that it becomes overidentified. It is argued in this paper that the contrary is true and that economic theory would require the inclusion of many more variables than those found in the existing econometric models so that the structural relationships included in these models are likely to be underidentified. Apparently "reasonable" overidentified structures have been obtained probably only because the specification errors arising from omission of relevant variables have cancelled one another. A consequence of the prevalence of underidentified structures is that the least squares reduced from equations are likely to be the best forecasting equations.